1. Field of the Invention
The present invention relates to oscillators.
2. Related Art
Many signal processing applications require real-time sine and cosine waveforms that are phase-locked in a quadrature relationship to one another. That is, the sine and cosine waveforms differ in phase from one another by 90 degrees. One such application is a radio receiver used to locate underground cables based on a magnetic signal transmitted from the cables. The radio receiver may include one or more frequency down-conversion stages (that is, heterodyning stages) to establish highly selective intermediate frequency (IF) and/or baseband signals. The heterodyning stages often use the above-mentioned sine and cosine signals to establish both in-phase (I) and quadrature (Q) IF and/or baseband signals.
One conventional oscillator capable of generating sine and cosine waveforms is based on a model of Simple Harmonic Motion (for example, using a model of a perfect spring-mass system with no damping). Typically, this oscillator requires a closed-loop including two series integrators and a negative feedback term. A frequency that solves for a loop gain equal to xe2x80x9cxe2x88x921xe2x80x9d determines an output frequency of the oscillator. One problem with this oscillator is that it is difficult to phase-lock the output sine and cosine signals in quadrature phase.
Another conventional oscillator is based on an unstable Infinite Impulse Response (IIR) filter. This is highly efficient computationally, but is limited by spectral distortion and difficulty in maintaining two phase-locked outputs.
Another known oscillator is based on a mathematical expansions of the terms sin(a+b) and cos(a+b). It is possible to construct a closed-loop coupled oscillator having a reasonably stable frequency output for two components (that is, the sine and cosine signals) phase-locked in quadrature with each other. When this approach is implemented using floating point arithmetic, Mantissa truncation leads to amplitude instability after many iterations. This problem worsens as floating point field widths become smaller, for example, when using a floating point field width of 32-bits. One known technique for reducing the amplitude instability is to implement a zero-crossing detector to reset amplitudes. This technique may be implemented on each signal zero-crossing or after a fixed number of oscillations. Although this technique improves long-term amplitude stability, the amplitude resetting process is non-linear, and disadvantageously causes undesired spectral distortion.
Therefore, there is a need for an oscillator that generates sine and cosine signals that are phase-locked to one another and separated in phase from one another by 90 degrees. There is a further need for such an oscillator to overcome the above-mentioned problems with known oscillators, such as amplitude instability and spectral distortion.
The present invention is directed to a quadrature oscillator that overcomes the problems in the prior art, mentioned above. The quadrature oscillator of the present invention produces sine and cosine waveforms that are phase-locked in quadrature to one another and have stabilized amplitudes. The sine and cosine waveforms each have improved spectral purity compared to known quadrature oscillators. The oscillator of the present invention is based on the expansions of sin(a+b) and cos(a+b). However, the oscillator of the present invention has improved amplitude stability, phase accuracy, and spectral purity, compared to known oscillators, such as the zero-crossing reset oscillator mentioned above. For example, in an application of the oscillator of the present invention, the oscillator improves receiver selectivity by as much as 25 decibels (dB) over the amplitude resetting type of oscillator mentioned above.
The oscillator of the present invention uses a resultant vector magnitude (sin2(xcex8)+cos2(xcex8)) from a previous iteration of the oscillator to act as negative feedback on an oscillator loop gain. The resultant magnitude represents stabilizes the amplitudes of the sine and cosine outputs of the oscillator.
An embodiment of the present invention is a method generating quadrature related waveforms. The method comprises generating a sine value, generating a cosine value, generating a magnitude value A equal to a sum of the squares of the sine value and the cosine value, and generating a negative feedback value as a function of the sine value, the cosine value, and the magnitude value. The method further comprises generating a next sine value using the sine value and the negative feedback value. The method further comprises repeating the just mentioned steps to generate a series of sine values representative of a sine wave. Further method steps result in generating a series of cosine values representative of a cosine wave. In an example application of the present invention, the sine and cosine waves are used in heterodyning stages of a locator receiver, to generate IF and/or baseband I and Q receiver signals.
Further embodiments of the present invention include a system and a computer program product for performing the above described method.
Further method, system and computer program product embodiments will become apparent from the ensuing description of the present invention.